We show that there is a family Schrdinger operators with scaled potentials which approximates the '-interaction Hamiltonian in the norm-resolvent sense. This approximation, based on a formal scheme proposed by Cheon and Shigehara, has nontrivial convergence properties which are in several respects opposite to those of the Klauder phenomenon.

Okumura proposed a candidate of post-quantum cryptosystem based on Diophantine equations of degree increasing type (DEC). Sizes of public keys in DEC are small, e.g., 1,200 bits for 128 bit security, and it is a strongly desired property in post-quantum erea. In this paper, we propose a polynomial time attack against DEC. We show that the one-wayness of DEC is reduced to finding special (relatively) short vectors in some lattices. The usual LLL algorithm does not work well for finding the most important target vector in our attack. The most technical point of our method is to heuristically find a special norm called a weighted norm to find the most important target vector. We call this method “weighted LLL algorithm” in this paper. Our experimental results suggest that our attack can break the one-wayness of DEC for 128 bit security with sufficiently high probability.

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In this paper, we present an efficient attack to the multivariate Quadratic Quasigroups (MQQ) cryptosystem. Our cryptanalysis breaks MQQ cryptosystems by solving systems of multivariate quadratic polynomial equations using a modified version of the MutantXL algorithm. We present experimental results comparing the behavior of our implementation of MutantXL to Magma's implementation of F_4 on MQQ systems (\ge 135 bit). Based on our results we show that the MutantXL implementation solves with much less memory than Magma's implementation of F_4 algorithm.

We show that the Masur–Veech volumes and area Siegel–Veech constants can be obtained using intersection theory on strata of Abelian differ- entials with prescribed orders of zeros. As applications, we evaluate their large genus limits and compute the saddle connection Siegel–Veech constants for all strata. We also show that the same results hold for the spin and hyperelliptic components of the strata.